getting to grips with the cost index(12)

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Since step climbs are performed in 4000ft altitude increments and since we aim to follow solution . (average between OPT and MAX FL), respective margins to 1.3g buffet limits are as for the various models.
By way of example, the best compromise between comfort and economy for the A340 is to step climb when reaching OPT FL -3000ft in order to level off at OPT FL +1000ft.
This step climb scenario is obviously not always feasible due to ATC trafficconstraints and external environment such as turbulence.
With the advent of FANS (Future Air Navigation System), the lateral track clearance will greatly facilitate using this optimization possibility by means of theoffset option available on every FMS.

6.2 Cross-over altitude versus optimum altitude
As per definition, the cross-over altitude is the altitude at which the climb law switches from Indicated Air Speed (IAS) to Mach speed (MACH).
For managed climbs on A320, A330, A340, the cross-over altitude varies with the cost index because of its influence on climb speeds.
The following Figure 15 is based on high take-off weights (MTOW -10t < TOW < MTOW). It illustrates the evolution of the cross-over altitude with the cost index for each Airbus type, summarizing climb laws with regard to IAS/MACH and True Air Speed (TAS).

For ISA deviations the following can be observed
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Temperature correction : For Upper Information Region (UIR) flight levels and TAS ranges (between 400 and 500kt), the TAS varies according to a simple rule :

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plus 1 kt per degree Celsius above ISA

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minus 1 kt per degree Celsius below ISA.

 

*  
Tropopause correction :

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In case of "high tropopause" (above FL 360), the figure shown above remains principally the same in terms of TAS advantage at cross-over altitude.

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In case of "low tropopause" (below FL 360), the TAS advantage, especially on A340, is no more advantageous if the tropopause altitude is below cross-over altitude since TAS will be constant (and much lower) from there on.

 

 

As per definition the Optimum Mach Number is a MN which remains greater than MRC and lower than LRC over the entire range of a typical cruise operation in terms of gross weight and altitude. The Optimum FL, for this Optimum MN, is the flight level which provides the greatest specific range (nm/kg) at a given gross weight. The Optimum FL increases with decreasing gross weight, as illustrated in the FCOM.
By design choice, and contrary to the rest of the Airbus fleet, the cost index has no influence on the climb IAS for the A340.
We also notice that, at cross-over altitudes, all aircraft demonstrate the best TAS since thereafter TAS decreases (up to the tropopause and is constant from there on) and since climb speed then becomes ECON MACH.
Let us now compare this cross-over altitude (taking into account an average altitude for the practical range of cost indices) to the first optimum altitude (considering a take-off weight close to the maximum authorized : i.e. between MTOW -10 tonnes and MTOW).
　
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